Electronic computer for transforming polar into rectilinear coordinates



5 Sheets-Sheet l Feb. 17, 1948. J. A. RAJCHMAN ELECTRONIC COMPUTER FOR TRANSFORMNG POLAR INTO RECTIIJINEAR COORDINATES Filed oct.

Feb. 17, 1948. J, A RAJCHMAN 2,436,178

ELECTRONIC COMPUTER FOR TRANSFORMING POLAR INT0 RECTILINEAR COORDINATES Filed Oct. 2l, 1943 5 Sheets-Shea?l 2 Summer (Ittorueg Feb.

' J. A. RAJCHMAN ELECTRONIC COMPUTER FOR TRANSFORMING POLAR INTO RECTILINEAR COORDINATES Filed 061'.. 21, 1943 5 Sheets-Sheet I5 Inventor Ciltorneg ELECTR C CO TER FOR TRANSFORMING POLAR TO RECTILINEAR COORDINATES Filed OGC. 2l, 1943 5 Sheets-Sheet 4 TTHZ/ZE/B v GMomcg Febo 17, 1948. 1, A RAJCHMAN 2,436,178

ELECTRONIC COMPUTER FOR THANSFORMING POLAR INTO RECTIMNEAR CooRDINATEs Filed Oct. 2l, 1945 5 Sheets-Sheet 5 mwutor Patented Feb. 17, 1948 ELECTRONIC COMPUTER FOR TRANSFORM- ING POLAR INTO REC'IILINEAR COORDI- NATES Jan A. Raichman, Princeton, N. J., assignor to Radio Corporation of America, a corporation of Delaware Application October 21. 1943, Serial No. 507,127

This invention relates generally to electronic computers, and particularly to an improved method of and means for converting the values of the polar coordinates of a point in space to binary quantities corresponding to the values of the rectangular coordinates of said point.

The present application is a continuation-inpart of application Serial No. 466,397, filed November 21, 1942.

Frequently the ring data obtained from artillery sighting apparatus is in the form of the polar coordinates of the target. It is often desirable to compute the ballistics equations incidental to sighting a gun in the terms of the rectangular coordinates of the target. Therefore. a continuously operated device which will provide the conversion from polar to rectangular coordinates is highly advantageous.

The angular and distance polar coordinates of the target may be translated into electrical data in the form of a combination of potentials corresponding to binary numbers. A binary number of p binary places can be represented by n potentials, each having one of two values Vi or V2 depending as to whether the corresponding digit is zero or one. These p potentials can be carried ona system of p conductors. The codal effect of the energization of these conductors to the potential V1 or V2 represents the binary number. 'I'he polar coordinates of a point are represented by a horizontal angle, a vertical angle, and a distance from a reference point on a reference line. The rectangular coordinates zc, y, z of the point may be obtained by deriving the gsines and cosines of the two angles and combining them to fulfill the conditions of the following equations:

=D sin e z=D cos e cos A 1l=D cos e sin A 4 Claims. (Cl. 23S-61.5)

`if the distance D is assumed to have unit value.

The particular values of the rectangular coordinates at any instant will ltherefore equal Dzo. Dxu and Dyo, respectively.

The above mentioned sines and cosines of the angles e and A may be obtained in terms of binary numbers by means of rotating discs provided with ducial marks calibrated in terms of the sine of the angle of rotation.

If a first shaft is rotated through the vertical angle e, and if the shaft is secured to a disc having light responsive iiducial marks in terms of the-binary numbers corresponding to the sine of the angle of rotation, a fixed mask including a slit disposed radially across the disc, will expose to voltage generating devices the iiducial marks representative of the sine of the angle e.

The first disc may be arranged to drive two other normally disposed discs of similar type. The last mentioned discs may be floated at their centers on a second shaft disposed normal to the iirst mentioned shaft. Slitted fixed masks, disposed at right angles to each other, may be secured to the second shaft adjacent each of the last mentioned discs. When the second shaft is rotated through an angle corresponding to the horizontal angle A, the slits in the lixed masks disposed adjacent each of the last mentioned discs will expose to voltage generating devices the ducial marks corresponding to the sine and the cosine of the angle of rotation A. The last menti-cned discs may be arranged to rotate in opposite directions in response to rotation of the rst shaft through the vertical angle e. It will therefore be clear that rotation of the shafts through the angles e and A, respectively, will unmask ducial marks characteristic of the sine of the angle e and the sine and cosine of the angles (A4-e) and (Af-e).

The ducial marks may be translated into electrical data as they rn'ove past the narrow slit in each mask and are exposed to light sources and light sensitive devices arranged on opposite sides of the discs carrying the fiducial marks. 'Ihe various duci'al scales, which will be described in detail hereinafter, will therefore activate predetermined ones of the light sensitive devices. depending upon the angular position of the par ticular mask with respect to the particular disc.

The electrical data so derived will be in the form of Xed voltages for any one position o1' the mask with respect to a selected disc. These voltages may be applied to an electronic counter, for example, of the type described in the copending application of George A. Morton and Leslie E.

Mory. Ber. No. 464,292, filed November 2, 1942. Patent No. 2,409,889, entitled Electronic computing devices. This copending application describes a means of adding and multiplying numbers represented through the medium of voltages representative of the different digits of the numbers. Voltages thus corresponding vizo the cosines of the sum and difference of the horizontal and vertical angles are applied to one of these counters. while voltages corresponding to the sines of the sum and difference of the angles are applied to a second such counter. As explained heretofore. the voltages derived in accordance with the instant invention Aare in terms of thev binary number corresponding to the value of the particular function.

A fourth disc may be secured to a shaft which is rotated through an angle proportional to the distance of the point in space from the reference point. The iiducial marks on the fourth disc may be arranged to actuate additional light sensit've devices, to provide voltages representative of the different digits of the number corresponding to this distance. n

The voltages thus corresponding to the lvalue of the sine of the angle e in terms of a binary number. and the voltages corresponding to the distance of the point. may be applied simultaneously to a iirst multiplier circuit of the type described in the copending application of Leslie E. ll'iory. Serial No. 467.229. med November 1l. 1942, now abandoned. which describes an electronic multinlying device for two or more binary numbers. The product derived from this first multiplier circuit will be equal to the binary value of the z rectangular coordinate of the point in space. Likewise, the output of the nrst cora r mentioned heretofore, and the voltages charaweristic of the binary value of the distance, may be applied to a second electronic multiplier circuit from whence the product will be proportional to the binary value of the :e coordinate of the point in space. Similarly. the output of the second counter and the voltages corresponding to the distance may be applied to a third electronic multiplier, from whence the binary equivalent of the y rectangular coordinate of the point may be derived.

Among the objects of the present invention is to provide an improved method of and means for converting the values of the polar coordinates of a `point in space to corresponding values of the rectangular coordinates of said point. Another object is to provide an improved method of and means for deriving electronically voltages reprel sentative of the digits of the binary numbers corresponding to the rectangular coordinates of a point in space when the polar coordinates of said point are known. A still further object of the invention is to provide an improved method of and means for deriving voltages representative of the digits of the binary values of the rectangular coordinates of a point in space when the polar coordinates of said points are available in terms of the angular displacement of two shafts corresponding to the angular polar coordinates of said point. and the angular displacement of a third shaft corresponds to the distance polar coordinate of said point.

'l'he apparatus, to be referred to in detail hereinafter, will be described by reference to the accompanying drawings. of which Figure l is a schematic circuit diagram of the invention which includes perspective views of the rotating discs: mure2isanelevationalviewofthearrange ment of the discs and light responsive apparatus; Figure 3 is a graph showing the polar and rectangular coordinates of a point in space with respect to the reference plane zOy; Figure 4 is an elevational view of one of the rotating discs in which ilducial marks are included: Figure 5 illustrates a modified form of disc: Figine illustrates a computing system adapted to perform the additions performed by the devices il and 2li of Fig. 1 and to perform the multiplications performedby the devices il, Il and Il of Pig. 1: Figure'iisawiringdiagramofasetupsystem which is part of the computing system of Pig. 6; and Figure 8 is a wiring diagram of the two lower orders of the computing system of Fig. 6. Similar reference numerals are applied to similar elements throughout the drawings.

Referring to Pig. 1. a shaft i. arranged to be rotated through an angle a corresponding to the vertical angle, is securely fastened to the center of a relatively thin. transparent disc 2 having fiducial marks characteristic of the binary value of the sine ofthe angle of rotation. A mask I.

having a narrow slit I, is rigidly supported so as to extend radially with respect to the disc 2, and is fixed in position. A plurality of light sources l are rigidly mounted in a fixed position adjacent one side of the disc f. while an equal number of light sensitive devices l are rigidly mounted in back of the slit l in such a manner that the radial position of each of the light sensitive devices corresponds to the radial position of one of the light sources.

A second shaft il is disposed normal to the first shaft I. in such a manner that their axes intersect. Second and third masks II and 23, which are arranged at right angles to each other, are rigidly connected to the second shaft ii in such a manner that they mask a second disc i2,

`which is floated at its center upon the second shaft ii. and the periphery of which is in contact with the periphery of the first disc 2.

l'iourth and fifth masking members Il and respectively, are `also securely fastened to the second shaft ii and arranged to mask a third disc 22, which also isfloated at its center on the second shaft il, and the periphery of which is in contact with the periphery of the first disc 2 at a point removed 1&0 degrees from the point of contact of the rst and second discs 2 and I2, respectively. A fourth disc l2 is fastened to a third shaft 2| and includes a nxed radial mask I8. Ught sources andlight sensitive devices (not all shown) are rigidly arrangedion the shaft Il or to other fixed supports so that the light from the sources passes through the narrow slits in each of the masks in such a manner that the fiducial marks on the various discs vary the light falling on the light sensitive devices which generate potentials characteristic of the binary number corresponding to the particular function of the angle.

lach of the individual light sensitive devices disposed adjacent the masking element It is connected to a first electronic adding circuit il of the type described hereinafter. Similarly. the individual light sensitive devices disposed adjacent the fourth masking element I) are also connected to the input of the first electronic counter circuit Il. whereby voltageseorresponding to the binary numbers which are representative of the sines of the sum and dierenee of the horizontal and vertical angles are applied to this adding circuit. In a like manner the individual light sensitive devices disposed adjacent the slits in the third and 1 l l l ilfth masking elements Il and Il are connected to the input of a second electronic adding circuit Il. -whereby voltages characteristic of the binary numbers corresponding to the cosines ci the sum and difference of the angles are applied to this adding circuit.

The individual light sensitive devices l, disposed adjacent the slit in the nrst masking elemasking element 53, are also connected to the input of the iirst multiplier unit 30, whereby the product of the binary quantities representative oi the sine of the vertical angle and the distance are multiplied to derive a product proportional tothe value of the rectangular coordinate z.` Similarly. the output of the first electronic adding circuit Il and the output of the individual light sensitive devices I8 are connected to the input of a second electronic multiplier circuit 40, whereby the product derived is proportional to the value on a second rectangular coordinate u. In like manner, the output of the'second electronic adding circuit 2l and the individual light sensitive devices Il are applied to the input of a third electronic multiplier circuit 50, from which a product is derived which ia proportional to the value of the :r rectangular coordinate. It should be un'- derstood that the digits of 'all values represented by voltages throughout the circuit are in terms of binary numbers characterized by the individual conditions of electronic circuits, such as trig-l ger circuits of the Eccles-Jordon type described in the above-mentioned copending applications. It should also be understood that the values on the $.11 and z coordinates derived from the multiplier circuits l0, 40 and l0, respectively, are also in terms of the electrical condition of trigger cir` cuitsof this type and are expressed in terms of binary numbers.

Fig. 2 is an elevational view which shows more clearly the constructional details of the rotating discs, masking elements and light responsive devices, already described. It should be understood that the particular constructional features dis closed herein are purely for the purpose of illus tration, and that various mechanical modiilcations may be employed without departing from the spirit and scope of the invention.

Fig. 3 isa graph illustrating the rectangular coordinates x, y and z, respectively, of a point P in space, located a distance D from'a reference point O ona reference line 01:. wherein the line OP forms -a vertical angle with its horizontal projection, and this projection forms an angle A with respect to a reference line 01:. The description included `heretofore refers to the point P as determined by the coordinates illustrated in the graph. i

Fig. 4 is" an elevational view of' a typical disc containing iiducial markings I representative of the binary value ofa function of the 'angle of ro'- tation of the disc. It should be understood that the particular characteristics and arrangement of the markings will be diiferent from'that illustrated and that the disc may be transparent with opaque ilduci'al markings, or vice versa Aor the disc may be arranged in `any other manner'to provide suitable actuation of. the light sensitive turc in a suitable mask. to a group of light sensitive devices. Various embodiments of light interrupters of this type are disclosed in the prior art. Similarly, the flducial markings may be placed upon a carrier such as a photographic nini wherein the distance of travel of the illm corresponds to the angular displacement of a shaft or to the distance of the point P from the reference point. as desired.

O the disc of Fig. 4, the negative values of the sine are given in terms of complementary numbers. 0n the disc of Fig. 5, they are given in their actual values, it being remembered that these values are negative for the two lower quadrants. 'I'he disc of Fig. 4 has the advantage that it is readily usuable with the adding systems |0 and 20 of Fig. 1 for the reason that a number A may be subtracted from a number B by adding the complementary A' to B and ignoring digital positions higher than the highest digital position of the number B. 'I'hus if B=10l1 and 4:0110, A inverted=1001+1=1010 and l011+1010- -l.010l. Ignoring the 1 in the highest place, there remains .0101 which is the difference between 0.1011 and 0.0110. The complementary of a binary number other than 0 is obtained by interchanging all digit zeros into ones and vice versa and adding one in the lowest devices described. For example, the disc may be i in the form of a reilector having non-reflecting nduclal marks and arranged to reflect light from suitably disposed light sources. through an aperplace. The additional place, on the high power side (left), indicated n parentheses, is necessary if complementary nu bers are used in additions or multiplcations. The table of the negative values of the disc ot Fig. 4 is as follows:

When an opaque sector of the disc is presented to a light source,- the resulting potential is representative of the binary digit zero and, when the presented sector is transparent, the resulting potential is representative of the binary digit one. The location of the digit with respect to the binary point is determined by the radial position of the sector. The pulses by which these resulting potentials are established are applied through the switches 5I to 55 to the set-up units of the various elements of the computing system of Fig. 8. This computing system is disclosed and claimed in a copending application of Leslie E. Flory, Ser. No. 507.131, led October 21, 1943.

'This computing system is operable either to add numbers, potentials representative of the various digits of which are applied to the set-up system including units 1 to VII, or to multiply two numbers, potentials representative of which are applied respectively to the units I to VII of one set-up system and to the units l0 to 13 of the other set-up system. As utilized to perform the functions of the devices Ill and 20 of Fig. 1, itis an adder or accumulator. As utilized to perform" the functions of the devices 30, 40 and 5i) "of Fig. 1, it is a multiplier.

The computing system includes a number of similarchannels. Thus.theiirstorlowestorder channel includes an input capacitor III, a setup unit I, a shift capacitor |20, transfer ampliner IIII. a differentiating circuit MII, and a totalizer unit comprising a set-up unit n, a carry-over amplifier |50 and a carry-over transformer lo. The connections of the first and second of these channels are shown in Fig. 8 in connection with which the operation of the system is hereinafter explained in detail. It should be understood at this point, however, that the amplifiers |30, ISI, etc., and |50, Ill, etc., are biased to cut on' when their corresponding set-up units are in a binary one condition and are biased below cutoff when their corresponding set up units are in a binary zero condition.

In the operation of the system to add numbers, pulses are applied through the capacitors III, IIB', etc., for establishing at the set-up unit output leads |24, I 25, etc., potentials representative of the first number which is then transferred to the set-up units XI, XII, etc., by touching the switch |28 to its lowermost contact. The first number is then removed from the set-up devices I, II, etc., by touching the reset switch si (Fig. 7) to its contact and pulses dependent on the digits of the second number are applied to the input capacitors I8, |I!, etc., thereby establishing at the least |24, |25, etc., potentials representative of the digits of the second number. This second number is then transferred to the set-up units XI, XII, etc.. by again touching the switch to its lowermost contact. When this operation has been repeated for each of the numbers to be added, potentials representative of the digits of their sum are available at the totalizer output leads L and are applied to the multiplier units 20, l! and 50 of Fig. 1.

Each of these multiplier units is similar to the system of Fig. 6. In the operation of this system Aas a multiplier, pulses dependent on the digits of the multiplicand are applied to the input capacitors IIS, IIB', etc., for establishing at the set-up unit output leads I2l, |25, etc., potentials representative of the digits of the multiplicand. Pulses dependent on the digits of the multiplier are likewise applied to the input terminals of the set-up devices 10, 1I, etc., for establishing at the contacts of the switch I2! to which the devices 10 to 1! are connected potentials representative of the digits of the multiplier.

With these potentials established as explained, the switch I2! is touched to the second contact from the bottom, thereby transferring the multiplicand to the set-up units XI. XII, etc., if the set-up unit 'III is in a binary one condition. Ii' the unit 'IIIis in a binary zero condition. however, nothing is transferred to the units 2U. XII, etc. The connections of the devices 'I0 to l! are similar to those o! the devices I. 1I, etc., with the exception that the stepping network may be omitted. Touching of the contact connected to the device 10, for example, transfers the multiplicand to the totalizer only when the unit lll is in a binary one condition because only then are the grid potentials of the ampliners I3! to Il! raised sumciently to pass an impulse. The same thing is true of the units 1I, 'I2 and 13. When the switch I2! engages its lowermost contact, the amplifiers I3! to I!! are likewise biased to a voltage at which pulses are passed to the units XI, X'II, etc., from the units I, II, etc., which are in a binary one condition. In either case, the next sumed (1) that the sure contact i'or the purpose of shifting the multiplicand by one digital position. The switch I2! is then touched to its third contact from the bottom. thereby transferring or not transferring the shifted multiplicand to the units XII. XIII, etc.. depending on whether the unit 'II is in a binary one or a binary zero condition. Thereafter, the switch I 2! is touched to its closure contact for again shifting the multiplicand by one digital position.

How the circuit of Fig. 8 functions in the apparatus of Fig. 1 will be understood if it is s'sdisks2. I2 and!! areofthe type shown by Fig. 5, (2) that successive terminals of this gure are connected to the successive Y capacitors IIB, III', etc., oi Fig. 8, and (3) that potentials `derived from the disk !2 and representative of the distance D are established in the set-up devices 10 to ll.

Under these conditions, the procedure of deriving the rectangular component z involves (1) moving the switch I2! to its ilrst contact thereby transferring the value sin e to the units XI, XII, etc., (2) closing and opening the switch I2! thereby sluiting the value of sin a by one digital position, (3) moving the switch I2! to its second contact thereby transferring the shifted value of sin e to the units In, XII, etc., and (4) continuing this process for the remaining digital positions oi the value of D. As a result of this procedure, there is established at the indicators of the units XI, XII, etc., a set of potentials representative of twice the value of the rectangular coordinate a which may be determined by reading the indicators with the binal point moved one digital position to the left.

By closure of the switches (one Ior each output lead of the disk 22 of Fig. l), the value of sin (A-e) is likewise established in the units step is the touching of the switch m to its cio- I, n. etc., of the devices I! and 40 of Fig, 1 and multiplied by the value of D so that potentials representative of the product D sin (A-) are established in the units XI, XII, etc. The units I, II, etc., are then reset to zero and the switchesv l! are closed to establish in the units I, II, etc., of the devices` I Il and of Fig. 1 potentials representative of the value of sin (A-I-e) which is multiplied by the value of D as previously explained to produce in the units XII, XII. etc., potentials representative of the product D Sill. (A+-e) The units XI. XII, etc., now have established in them potentials representative of the sum [D sin(A-E) ]+[D sin (A+) ]=D[sin (A-E)+ sin A+l :twice the value of the rectangular coordinate u which is derived by moving the binal point one digital position to the left.

In the same way, the sum of is established in the umts XI, XII, etc. This sum is equal to twice the rectangular coordinate :c and must be read with the binal point moved one digital position to the leit in order to produce the true value of z.

As indicated by Fig. 1, the switches l! (one for each digital position of the value of sin (A-el) and the switches II (one for each digital position of the value of cos '(4-0) may be simultaneously operated as indicated by a broken and D cos (A-e) are simultaneously established in the units III-40 and ZIB-III. In the same way, the switches 52 and M may be simultaneously operated toestablish the value of D sin (A4-e) in the units |40 and the value of D cos (A-I-e) in the units -00.

When these operations have been repeated for each digit of the multiplier, potentials representative of the product are available at the output leads L so that the three groups of potentials represent respectively the digits of numbers which are double the correct values oi' the a', y and e coordinates of the point P (Fig. 3). 'I'he real values are derived with sumcient accuracy by moving the binal point one digital position to the left.

The connections of the set-up units (Fig. '1) and their operation are for the most part familiar to those skilled in the art and are readily understood without detailed explanation.

Thus, each unit includes a pair of electron discharge devices |0||02, |||-||2, |2|-|22, etc. Each pair oi' devices is so interconnected that only one of the devices is conducting at a given time. Current may be transferred from one device of a pair to the other by applying a negative pulse between the terminals I I5. When the device |0I (in the case of unit I) is conducting, the unit I is in a binary one condition as indicated by the lighting of the lamp ||2. When the device |02 is conducting, the unit I is in a binary zerocondition. The same is true for all the other units which are arranged to provide at their output terminals I24-|20, etc., potentials representative o1' successive digits of the number to be added or multiplied.

One feature not so well known to those skilled in the art is the reset system by which a negative pulse is applied through a switch sl and resistors ||1, 8, I0, etc., to the grids of the devices |0I, I, |2|, etc., for establishing all the units in a binary zero condition.

Another feature not so well known is the multiplicand shift system by which a negative pulse is applied through the capacitors |20, |20', |20", etc., to the control grids of the tubes |0I, and |2| for shifting multiplicand one digital position as previously indicated. In explaining the operation of this shift system, it is assumed that the tubes |0I, III and |22 are conducting. This condition of the circuit represents the binary number 011. In the system of Fig. 7, the unit I0|I02 is intended to represent the lowest order of the binary number, the unit II I2 the next to the lowest order of the number, etc.

The application of a negative pulse through the capacitors |20, |20' and |20" operates to make the tube |02 conducting and the tube |0| non-conducting. It does not affect the condition of the tube |2| for the reason that this tube is already non-conducting, It starts to make.;.the tube III non-conducting thereby producing a positive pulse which operates through the capacitor |23' to make the tube |2| conducting and the tube |22 non-conducting. The tube III, however, is prevented from assuming a non-conducting state due to a positive pulse applied to its grid from the anode of the tube |0| through the capacitor |22 which may have a capacity of 100 paf. as compared to a capacity of the order of 3 paf. for the capacitors |20, |20', |20", etc.

The circuit is now in a condition representing the binary number 110. the number having been shifted one digital position to the left.

If it be assumed that the tubes |0I, ||2 and |22 are conducting, the binary number set up in the circuit is 001. Under these conditions, the application of a negative pulse through the cato cutoii'. The pulse |40 pacitors |20, |20 and |20" causes current to be transferred from the tube |0| to the tube |02 but has no eiiect on the tubes III and |2I. When current is transferred from the tube |0| to the tube |02, however, a positive pulse originating at the anode of the tube |0| is applied through the relatively large capacitor |22 to the grid oi' the tube thereby transferring current from the tube ||2 to the tube Under these conditions, the binary number now set up in the circuit is 010, the number having been shifted one digital position to the left.

Fig. 8 as previously indicated, is a wiring diagram oi' the two lower order channels of Fig. 6, corresponding parts being identified by the same reference numerals in the two figures.

In the operation of these channels. a number is set up in the units I, II, etc., by applying to the contacts ||0 pulses dependent on the various digits oi' the number, positive pulses are applied through the switch |20 for transferring the number to the totalizer set-up devices XI, XII, etc.. and negative impulses are applied through the switch |29 for shifting the number by one digital position only when numbers are to be multiplied.

Thus assuming the binarynumber 01 to be set up in the units I and II and the set-up devices XI, XII, etc., to be in a binary zero position, amplifier |2I, |00 and |0| are biased below cutoii' and the ampliiier |20 is biased to cutoil. Under these conditions, the application of a positive pulse through the switch |28 operates through amplier |20. diode |00 and capacitor 10 to apply a negative pulse tothe unit XI whereby this unit is converted to a binary one condition and the amplifier `|00 is biased to cutoil'. This follows as a result of the more negative voltage applied to the cathode of the diode I 00 and to the grid of the ampliiier |00 when through the anode resistor of the amplifier |20.

A second positive pulse applied through the switch |20 operates through the amplifier |30 and theA differentiating circuit |40 to produce positive and negative pulses 41 and |40 (see Fig. 6). The pulse |41 operates through the ampliiier |00, the capacitor |12, the diode |0| and the capacitor |1| to change the unit XII to a binary one condition and to bias the amplifier I0| operates through the diode |00 and the capacitor 10 to change the unit XI to a binary zero condition, thereby biasing the amplifier |00 beyond cutoi.

A third positive pulse applied through the switch |20 operates, as in the case of the first pulse, to change unit XI to a binary one condition and to bias the ampliier 00 to cutoi.

A fourth positive pulse applied through the switch |20 operates through the amplifier` |20 and the differentiating circuit |40 to produce the positive and negative pulses |41 and |40. The positive pulse |41 operates through the transformer 00 and the ampliiler ISI to apply a negative pulse to the unit XIII (Fig. 6) whereby it is converted to a binary one condition and the ampliiier |02 is biased to cutoil and `vthrough the capacitor |12, the diode |0| and the capacitor |1| to apply a negative puise to unit XII whereby it is converted to a binary zero condition and the amplier I0| is biased beyond cutoii.` The negative pulse |40 operates through the diode |00 and the capacitor |10 to apply a negative pulse to the unit XI whereby it is converted to a binary zero condition and the amplifier |00 is biased beyond cutoi.

A fth positive pulse applied through the current is drawn l1 switch |20 operates as in the cases f the nrst er'ithird tochanseunitxltoabinary one condition and to bias the amplifier les to cutoif.

Thus the application or five pulses has operated tosetupinthcunits nmetddbinarynumber 101 (5 in the decimal system) which is the sum of the numbers transferred from the set-up system I, II, ete., to the set-up system 1H, XII

Had the appli pulses been potentials representative of the digits of a multiplier, the switch 20 would have been touched to its closure contact after each transfer or non-transfer to shift the binary number l by one digital position so as to set upthe resulting product in the units XI, XII. etc.

As is apparent from the foregoing discussion, an outstanding of the present invention is the provision of an improved apparatus and method of operation whereby trigonometric functions characteristic of the polar coordinates of a point are converted to the rec'- tangular coordinates to such polar coordinates.

I claim as my invention:

1. A computer for translating the values of thepolar coordinates oi a point in space into voltages` representative o! the rectangular coordinates of said point which includes a first supporting means, va second supporting means, at least one fiducial scale representative of a predetermined function of an angular polar coordinate of said point on each of said supporting means, cooperative masking means respectively including a slit disposed in operable relation to said scales of both of said supporting means, means for displacing said first supporting means an amount representative of a nrst angular polar coordinate of said point, means for displacing said second supporting means an equal amount in the opposite sense, means for displacing said maskof the totaliler.

ing means an amount representative of a second angular polar coordinate of said point, iirst separate voltage generating means responsive to the exposed ilducial marks of each iiduciai scale on said first supporting means, second separate voltage generating means responsive to the exposed nduclal marks of each fiducial scale on said second supportingmeans, means responsive to said generated voltages for deriving potentials representative of thedigits of the value of a predetermined function of the sum and difference of said angles, means for deriving voltages representative of the digits of the value of the distance polar coordinate of said point, and means for deriving the product ol said distance and said predetermined function of said combined angles.

2. In a device for converting the polar coordinates D, A and e into rectangular coordinates z. u and z, the combination of means including three members bearing fiduciary marks and rotatable together, means for deriving from said marks pulses in groups which are respectively representative of the values of D, the sines of (A+e) and (A-e) andthe cosines of (A-l-e) and (A-a); means for deriving the sum of said sine (A+.) representative pulses and said sine (A-) representative pulses, means for deriving the sum of said cosine (A+r) representative pulses and said kcosine (A- pulses, and means for multi- Flying each of said sum representative pulse groups and said sine a pulse representative group by said D representative puise group to derive l2 other groups oi pulses which are representative ofthe valuesofzsandkrespectively.

3. In a device for converting the polar coordinates D, A and into rectangular coordinates 2. y and s, the combination of means including three members bearing fiduciary marks and rotatable together, means for deriving from said marks pulses in groups which are respectively representative of the values of D, the sines of e, (A4-c) and (A-a) and thecosines of (A4-e) and (d-a): electronic means for deriving groups of pulses respectively representative of the sum of said sine (A4-ci and sine (A-e) representative pulses and the sum of said cosine (A+) and cosine (A- representative pulses; and means for deriving groups of pulses which are the products of said D representative pulses multiplied by said sine c representative pulses, said D representative pulses multiplied by said sine representative pulses and said D representative pulses multiplied by said cosine `representative pulses.

a. `In a device for converting the polar coordinates D, A and u into rectangular coordinates .'c, y and z, the combination of a first member rotatable in accordance with the value o! and bearing marks representative of sine of e, means selectively responsive to said marks for producing electrical pulses representative of diiferent values of the sine of a, second and third members rotatable by said iirst member in opposite directions in accordance with the value of A and bearing marks representative of the sine and the cosine of A, means selectively responsive to the marks of said second member for producing electrical pulses representative of sine v(A4-0 and cos (A-l-a), means selectively responsive to the marks of said third member for producing elecn trical pulses representative of sine (A-o and cosine (i4-a), means for deriving a first sum of pulses equal `to said sine (r4-c) plus said sine (A+a) representative pulses, means for derivmgasecondsumofmlisesequaltosaid cosine (A- plus said cosine (A4-c) pulses, a fourth member rotatable in accordance with the value of D and bearing marks representative of D, means selectively responsive to said D representative marks for producing pulses representative of diilerent `values of D, and means for deriving products respectively equal to the number of said D representative pulses times the number of said sine a representative pulses, the number of said D representative pulses times the number o! said ilrsthsum representative pulses and the number of said D representative pulses times the number of said second sum representative pulses,

JAN A. RAJCHMAN.

REFERENCES CITED The following references are oi record in the ille of this patent:

UNITED STATES PATENTS Number Name Date 2,307,868 Stibits Jan. i2, i943 2,318,591 Coumgnal May l1, i943 2,080,186 Reymond May 11, 1937 2,408,081l Lovell et al Sept. 24. 1946 FOREIGN PATENTS Number Country Date 164,785 Great Britain 1919 

